Linear Algebra and Matrix Analysis for Statistics

Assuming no prior knowledge of linear algebra, this self-contained text offers a gradual exposition to linear algebra without sacrificing the rigor of the subject. It presents both the vector space approach and the canonical forms in matrix theory. The book covers important topics in linear algebra that are useful for statisticians, including the concept of rank, the fundamental theorem of linear algebra, projectors, and quadratic forms. It also provides an extensive collection of exercises on theoretical concepts and numerical computations.

Zusatztext "? a unique and remarkable book ? has much to offer that is not found elsewhere. ? In Linear Algebra and Matrix Analysis for Statistics! Sudipto Bannerjee and Anindya Roy have raised the bar for textbooks in this genre. For me! this book will be an invaluable resource for my teaching and research. ? an outstanding choice for research-oriented statisticians who want a comprehensive theoretical treatment of the subject that will take them well beyond the prerequisites for the study of linear models."-Journal of the American Statistical Association! Vol. 110! 2015"The sixteen chapters cover the full range of topics ? Topics are presented in a logical order and in a reasonable pace. The book is compactly written and the approach throughout is rigorous! yet well readable. ? an excellent introduction to linear algebra."-Zentralblatt MATH 1309"This would be a reasonable candidate for use in a standard linear algebra course! even at institutions with no statistics majors. ? The proofs are very detailed and the authors bind the argument together with clear text that flows beautifully. ? Some linear algebra courses put a greater emphasis on concrete applications or on using software to get computations done. Other texts treat linear algebra as a branch of abstract algebra and allow spaces over arbitrary fields. This book is a strong contender for the vast majority of linear algebra courses that fall between those two extremes."-MAA Reviews! October 2014"This beautifully written text is unlike any other in statistical science. It starts at the level of a first undergraduate course in linear algebra! and takes the student all the way up to the graduate level! including Hilbert spaces. It is extremely well crafted and proceeds up through that theory at a very good pace. The book is compactly written and mathematically rigorous! yet the style is lively as well as engaging. This elegant! sophisticated work will serve upper-level and graduate statistics education well. All and all a book I wish I could have written."-Jim Zidek! University of British Columbia! Vancouver! Canada Informationen zum Autor Sudipto Banerjee, Anindya Roy Klappentext Assuming no prior knowledge of linear algebra, this self-contained text offers a gradual exposition to linear algebra without sacrificing the rigor of the subject. It presents both the vector space approach and the canonical forms in matrix theory. The book covers important topics in linear algebra that are useful for statisticians, including the concept of rank, the fundamental theorem of linear algebra, projectors, and quadratic forms. It also provides an extensive collection of exercises on theoretical concepts and numerical computations. Zusammenfassung Linear algebra and the study of matrix algorithms have become fundamental to the development of statistical models. Using a vector space approach, this book provides an understanding of the major concepts that underlie linear algebra and matrix analysis. Inhaltsverzeichnis Matrices, Vectors, and Their Operations. Systems of Linear Equations. More on Linear Equations. Euclidean Spaces. The Rank of a Matrix. Complementary Subspaces. Orthogonality, Orthogonal Subspaces, and Projections. More on Orthogonality. Revisiting Linear Equations. Determinants. Eigenvalues and Eigenvectors. Quadratic Forms. The Kronecker Product and Related Operations. Linear Iterative Systems, Norms, and Convergence. Abstract Linear Algebra. References. ...

" a unique and remarkable book has much to offer that is not found elsewhere. In Linear Algebra and Matrix Analysis for Statistics, Sudipto Bannerjee and Anindya Roy have raised the bar for textbooks in this genre. For me, this book will be an invaluable resource for my teaching and research. an outstanding choice for research-oriented statisticians who want a comprehensive theoretical treatment of the subject that will take them well beyond the prerequisites for the study of linear models."Journal of the American Statistical Association, Vol. 110, 2015 "The sixteen chapters cover the full range of topics Topics are presented in a logical order and in a reasonable pace. The book is compactly written and the approach throughout is rigorous, yet well readable. an excellent introduction to linear algebra."Zentralblatt MATH 1309 "This would be a reasonable candidate for use in a standard linear algebra course, even at institutions with no statistics majors. The proofs are very detailed and the authors bind the argument together with clear text that flows beautifully. Some linear algebra courses put a greater emphasis on concrete applications or on using software to get computations done. Other texts treat linear algebra as a branch of abstract algebra and allow spaces over arbitrary fields. This book is a strong contender for the vast majority of linear algebra courses that fall between those two extremes."MAA Reviews, October 2014 "This beautifully written text is unlike any other in statistical science. It starts at the level of a first undergraduate course in linear algebra, and takes the student all the way up to the graduate level, including Hilbert spaces. It is extremely well crafted and proceeds up through that theory at a very good pace. The book is compactly written and mathematically rigorous, yet the style is lively as well as engaging. This elegant, sophisticated work will serve upper-level and graduate statistics education well. All and all a book I wish I could have written."Jim Zidek, University of British Columbia, Vancouver, Canada

Autorentext

Sudipto Banerjee, Anindya Roy

Zusammenfassung
Linear algebra and the study of matrix algorithms have become fundamental to the development of statistical models. Using a vector space approach, this book provides an understanding of the major concepts that underlie linear algebra and matrix analysis.

Inhalt

Matrices, Vectors, and Their Operations. Systems of Linear Equations. More on Linear Equations. Euclidean Spaces. The Rank of a Matrix. Complementary Subspaces. Orthogonality, Orthogonal Subspaces, and Projections. More on Orthogonality. Revisiting Linear Equations. Determinants. Eigenvalues and Eigenvectors. Quadratic Forms. The Kronecker Product and Related Operations. Linear Iterative Systems, Norms, and Convergence. Abstract Linear Algebra. References.